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Proceedings ArticleDOI

Closed Form Solution of Perspective 3-Point Problem (P3P) Based on Algebraic Resultant and SVD

TLDR
The paper puts forward the algebraic resultant to analytically determine the camera-point (camera projective center to control point) distances, and presents the closed form solution of camera position and orientation based on SVD.
Abstract
Perspective 3-point problem (P3P) is one of the most fundamental issues in computer vision and photogrammetry. The paper puts forward the algebraic (multipolynomial) resultant to analytically determine the camera-point (camera projective center to control point) distances, and presents the closed form solution of camera position and orientation based on SVD. The numerical case study shows the approach is correct and efficient for the case of arbitrary pose angles image.

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References
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Journal ArticleDOI

Closed-form solution of absolute orientation using unit quaternions

TL;DR: A closed-form solution to the least-squares problem for three or more paints is presented, simplified by use of unit quaternions to represent rotation.
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Closed-form solution of absolute orientation using orthonormal matrices

TL;DR: In this paper, a closed-form solution to the least square problem for three or more points is presented, which requires the computation of the square root of a symmetric matrix, and the best scale is equal to the ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids.
Journal ArticleDOI

Linear N-point camera pose determination

TL;DR: This work proposes a family of linear methods that yield a unique solution to 4- and 5-point pose determination for generic reference points and shows that they do not degenerate for coplanar configurations and even outperform the special linear algorithm for copLANar configurations in practice.
Journal ArticleDOI

Solving systems of polynomial equations

TL;DR: The author presents an algorithm for solving polynomial equations using the combination of multipolynomial resultants and matrix computations, which is efficient, robust and accurate.
Book

Close Range Photogrammetry

TL;DR: This book provides a thorough presentation of the methods, mathematics, systems and applications which comprise the subject of close range photogrammetry, which uses accurate imaging techniques to analyse the three-dimensional shape of a object.
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